In August 1859, a 32-year-old, timid, bashful, sensitive, diffident soul, with a horror for speaking in public, was presenting a paper to the Berlin Academy about the density of prime numbers on the real line. The brilliant mathematician giving the historic lecture was Bernhard Riemann, and in the course of the talk he made an incidental remark, which to this day has remained an enigma, known as the Riemann hypothesis (RH). The hypothesis simply states that Riemann zeta function, an elegantly expressed analytic function, has all the complex zeros on a vertical line in the complex plane. Riemann zeta function has been a fascinating subject of study for generations of mathematicians because of its intimate connection with prime number theory.

If we recognize that what RH is really saying is that the reciprocal of the zeta function has for its abscissa of convergence, the line s=1/2, we can reformulate the hypothesis and give a network-theoretic equivalent of the RH. The reference given below gives the hypothesis in terms of the power dissipated in an electrical network.